270 Prof. Oliver Lodge on the Seat of the Electromotive 



generated or destroyed per unit current. And the whole 

 E.M.F. of a circuit is simply the algebraic sum of all such 

 E.M.F.'s at every point of the circuit. 



If we must put it into symbols, there is a slope of potential, 

 dE = ®(t)dt, at any point of either metal (considering J as 

 unity, i. e. that heat is measured in mechanical units) ; and at 

 a junction, where a finite amount of heat, C . II (£), is produced, 

 a finite E.M.F. exists, 



AE=n(f). 



The whole E.M.F. of a simple circuit is made up of four 

 portions, one portion at each junction, and the rest in each 

 metal wherever there is a temperature-slope, 



E = (AE),+ fdE-(AE) s -fdE 

 Jb Ja 



And the second law of thermodynamics -J cycle 1 — = > , 



combined with this, gives us further the simple relation 

 among these quantities already established, 



n = ^E 



t ~~ dt } 



©a-®b __^ 2 F 



t ~~ di 2 ' 



And, as before, if the last expression is to be constant, 

 B=J(*i-*) + i«W-©' 



* Perhaps the shortest way of putting the whole thing ah initio is as 

 follows : — Regard the difference of the Thomson functions in the two 

 metals as a single function ; i. e. write for 0a(£) — ©bCO simply 0. Then 

 the second law of thermodynamics (in its differential form) gives us 



S =/'(*), . . .(i), f =*'(*>; ... (ii) 



where/ and <£ are unknown functions satisfying the condition 



or 



/"=*' (iii) 



Further, by the first law of thermodynamics and the energy definition of 

 E.M.F., 



Essl^-Ha+J edt, 



